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Energy-Efficient Joint User-RB Association and Power Allocation for Uplink Hybrid NOMA-OMA

Ming Zeng, Animesh Yadav, Octavia A. Dobre, H. Vincent Poor

arXiv:1903.05756v1cs.ITmath.IT

TL;DR

The paper studies how to maximize energy efficiency in uplink hybrid NOMA-OMA while meeting each user's minimum-rate requirement. It jointly optimizes user-RB association and power allocation, then reports that its proposed scheme outperforms other HMA- and OMA-based algorithms.

  • Problem

    The paper addresses joint user clustering, channel assignment, and power allocation for energy-efficient uplink hybrid access under per-user minimum-rate requirements.

    Source: §I · pp. 3–4

  • Method

    A many-to-one bipartite-graph swap-matching scheme jointly selects user-RB associations and power, with separate low-complexity energy-efficiency optimization for a fixed association.

    Source: §I · p. 4, §IV · p. 8, B. Maximizing the EE when (6) is… · pp. 11–12

  • Results

    The proposed joint association and power-allocation scheme outperforms other HMA- and OMA-based algorithms in the reported simulations.

    Source: §I · p. 4, B. Multiple clusters · p. 23

  • Takeaways & Limitations

    The proposed power-allocation algorithm obtains optimal energy efficiency for any SIC order and an arbitrary number of users when the fixed-association problem is feasible.

    Source: §I · p. 4

Abstract

from arXiv · show

In this paper, energy efficient resource allocation is considered for an uplink hybrid system, where non-orthogonal multiple access (NOMA) is integrated into orthogonal multiple access (OMA). To ensure the quality of service for the users, a minimum rate requirement is pre-defined for each user. We formulate an energy efficiency (EE) maximization problem by jointly optimizing the user clustering, channel assignment and power allocation. To address this hard problem, a many-to-one bipartite graph is first constructed considering the users and resource blocks (RBs) as the two sets of nodes. Based on swap matching, a joint user-RB association and power allocation scheme is proposed, which converges within a limited number of iterations. Moreover, for the power allocation under a given user-RB association, we first derive the feasibility condition. If feasible, a low-complexity algorithm is proposed, which obtains optimal EE under any successive interference cancellation (SIC) order and an arbitrary number of users. In addition, for the special case of two users per cluster, analytical solutions are provided for the two SIC orders, respectively. These solutions shed light on how the power is allocated for each user to maximize the EE. Numerical results are presented, which show that the proposed joint user-RB association and power allocation algorithm outperforms other hybrid multiple access based and OMA-based schemes.

I. INTRODUCTION

The paper addresses energy-efficient uplink NOMA with OMA resources, motivated by limits of prior power-allocation work and practical constraints on applying NOMA to all IoT devices. It models user and RB assignments jointly with power allocation under per-user minimum-rate requirements.

I. INTRODUCTION

  • Prior uplink power-allocation schemes target spectral efficiency, and cited multi-carrier methods either assume equal channel gains across subcarriers or support only two users per subcarrier.The paper instead studies energy efficiency in a hybrid NOMA-OMA system, motivated by device bandwidth limits, decoding delay, and SIC error propagation as cluster size grows.Source: §I · pp. 3–4
  • Jointly choosing user clustering, channel assignment, and power allocation makes the energy-efficiency problem non-convex and challenging.The paper proposes a many-to-one bipartite-graph swap-matching scheme and reports that it outperforms other HMA- and OMA-based algorithms.Source: §I · p. 4

A. System model

  • Each RB can serve multiple users through NOMA, while each user accesses only one RB; users sharing an RB form a cluster.The system equally divides bandwidth among RBs and models user channels with large-scale path loss and small-scale Rayleigh fading.Source: A. System model · pp. 4–5

B. Problem formulation

  • The objective is to maximize system energy efficiency while meeting each user's minimum-rate requirement and individual maximum transmit-power constraint.Each cluster's energy efficiency is its achievable sum rate divided by total consumed power, including fixed circuit and flexible transmit power.Source: B. Problem formulation · p. 6

III. JOINT USER-RB ASSOCIATION AND POWER ALLOCATION (PA)

The joint user-RB association and power-allocation problem is non-convex and involves interference across clusters. The proposed swap-matching algorithm accepts swaps that improve the involved RBs' total energy efficiency and converges after finitely many swaps.

III. JOINT USER-RB ASSOCIATION AND POWER ALLOCATION (PA)

  • The joint problem is difficult because reassignment affects other users through intra-cluster interference, while its objective is non-convex.The stated total complexity is O(U^2(I1X + M)), where I1 is the number of swap-matching iterations and X is the complexity of power allocation for calculating energy efficiency.Source: §III · pp. 6–7, B. Convergence and complexity · p. 8

A. Proposed algorithm

  • The algorithm models users and RBs as the two node sets of a bipartite graph and exchanges RB assignments between users matched to different RBs.A swap is approved only if the sum of the energy efficiencies for the two involved RBs increases after power allocation is updated.Source: A. Proposed algorithm · p. 7

B. Convergence and complexity

  • The proposed joint user-RB association and power-allocation algorithm converges after a finite number of swapping operations.Each approved swap increases system energy efficiency, which has an upper bound under limited power and spectrum resources.Source: B. Convergence and complexity · p. 8

IV. POWER ALLOCATION UNDER GIVEN USER-RB ASSOCIATION

With user-RB association fixed, the paper separates energy-efficiency optimization across clusters because their RBs are orthogonal and cluster energy efficiencies are mutually independent.

IV. POWER ALLOCATION UNDER GIVEN USER-RB ASSOCIATION

  • For a fixed user-RB association, maximizing system energy efficiency is equivalent to maximizing energy efficiency separately for each cluster.The clusters are mutually independent because they use different RBs.Source: §IV · pp. 8, 10
  • The power-allocation routine is used by the joint association algorithm to evaluate energy efficiency under a given user-RB association.The number of iterations for the association algorithm to reach its final matching is not available in closed form.Source: §IV · p. 8

A. Determine the feasibility

Feasibility is determined by whether minimum-rate requirements can be met within users’ power constraints. When feasible, the paper develops EE power-allocation methods, including a low-complexity optimal algorithm and results on power transfers and analytical limits.

A. Determine the feasibility

  • The problem is feasible when the minimum-rate requirements and power constraints are all satisfied.The feasibility test derives the minimum power required for each user, starting with the last SIC-decoded user and extending to all users.Source: A. Determine the feasibility · pp. 10–11

B. Maximizing the EE when (6) is feasible

  • The EE objective has a strictly concave numerator and an affine denominator, making it strictly pseudo-concave and amenable to Dinkelbach optimization.The resulting problem has an affine power constraint.Source: B. Maximizing the EE when (6) is… · p. 11
  • The low-complexity power algorithm starts each user at minimum required power, then updates users one by one until convergence to the global optimum.The objective increases or stays unchanged after each update, and the paper gives complexity O(I3) for convergence.Source: B. Maximizing the EE when (6) is… · p. 12
  • Algorithms 2 and 3 also apply to EE maximization under any SIC order.The paper states that other SIC orders have the same objective and convex minimum-rate constraints.Source: B. Maximizing the EE when (6) is… · pp. 12–13
  • Transferring power from a lower-gain user to a higher-gain user increases EE.The sum transmit power—and thus the denominator—remains unchanged while the numerator increases.Source: B. Maximizing the EE when (6) is… · p. 13
  • Analytical results for intermediate cases are complicated by coupling between QoS requirements and power constraints.The paper derives insights for two extreme cases, but identifies this coupling as a barrier to analytical results between them.Source: B. Maximizing the EE when (6) is… · p. 15

V. TWO USER CASE

For two users, analytical power-allocation solutions are possible. The paper treats the two SIC orders separately because their feasibility regions differ.

V. TWO USER CASE

  • For the special case of two users, analytical EE power-allocation solutions are possible although the general multiple-user case is challenging.The two-user derivatives yield three cases to consider.Source: §V · p. 16
  • The analysis considers three cases based on the derivatives of EE with respect to the two users’ powers.Source: §V · p. 16
  • The two SIC orders have different feasibility regions and therefore require separate power-allocation solutions.The paper labels the order decoding user 1 first as Case I and the other order as Case II.Source: §V · p. 16

A. Analytical solution when user 1 is decoded first

For the two-user solution when user 1 is decoded first, the paper gives phase-dependent power behavior and identifies bisection as the dominant computation for finding the EE solution.

A. Analytical solution when user 1 is decoded first

B. Analytical solution when user 2 is decoded first

For the alternative SIC order, the two-user allocation is reduced to a single-variable EE function, while QoS constraints can make power feasibility and EE depend on decoding order.

B. Analytical solution when user 2 is decoded first

VI. SIMULATION RESULTS

The simulations are presented as verification of the developed results, using default parameters and uniform user constraints.

VI. SIMULATION RESULTS

  • The simulations are conducted to verify the developed results.Source: §VI · p. 19
  • Default simulation parameters are listed in Table III.Source: §VI · p. 19
  • All users are assigned the same minimum-rate requirements and maximum-transmit-power constraints in the simulations.Source: §VI · p. 19

A. Single cluster

The simulations compare NOMA and OMA across channel-gain differences, user counts, and power constraints; outcomes vary with those conditions. They also compare the SIC orders and analytical power solutions.

A. Single cluster

  • As maximum transmit power rises, EE first increases for MaxEE and MaxSE, then MaxEE saturates while MaxSE continues to decrease.Source: A. Single cluster · p. 19
  • With larger channel-gain differences, NOMA achieves much higher EE than OMA for both two- and three-user cases, while two users outperform three in both schemes.Source: A. Single cluster · p. 19
  • For smaller channel-gain differences under low maximum power, OMA outperforms NOMA because NOMA interference reduces the feasible power region under QoS constraints.For the two-user example, NOMA user 2 cannot transmit at full power while ensuring user 1's QoS.Source: A. Single cluster · p. 19
  • Case I achieves much higher EE than Case II when comparing the two SIC orders.Source: Figure 3 · p. 20, A. Single cluster · p. 21
  • Without QoS constraints, NOMA is always better than OMA, although its gain is minor in the two-user case; NOMA also outperforms OMA at high maximum power.Source: A. Single cluster · pp. 20–21
  • Algorithm 2 and the analytical solution produce the same power results; increasing maximum power moves Case I from Phase I to IV and Case II from Phase I to III.At low maximum power, user 1 in Case I and user 2 in Case II transmit at full power.Source: A. Single cluster · p. 21

B. Multiple clusters

In multiple-cluster simulations, HMA-prop leads the compared schemes, while the HMA-over-OMA advantage does not necessarily grow with channel-gain differences. Doubling the users and RBs yields more than twice the EE for all schemes except HMA-rand, with fewer than 60 swaps needed for convergence in the larger setting.

B. Multiple clusters

  • The comparisons include OMA-swap, OMA-MWM, HMA-DC, HMA-MWM, and HMA-rand, with OMA-MWM alternating association and power updates.HMA-DC uses preferred-RB requests; HMA-rand assigns users randomly.Source: B. Multiple clusters · pp. 21–23
  • Across both channel-gain cases, HMA-prop ranks best among six schemes, but larger gain differences do not guarantee a larger HMA-over-OMA advantage.The paper attributes this qualification to different user-RB associations under HMA and OMA.Source: Figure 5 · p. 22, B. Multiple clusters · p. 23
  • More than twice the EE is obtained when scaling from 12 users and 4 RBs to 24 users and 8 RBs, except for HMA-rand.The authors identify this as a multiplexing gain from having more RBs.Source: Figure 6 · p. 22, B. Multiple clusters · p. 23
  • Fewer than 60 swaps suffice for convergence with 24 users and 8 RBs, although swap counts grow with the number of RBs.Figure 7 plots the CDF of swaps needed across the two scenarios.Source: B. Multiple clusters · p. 23, Figure 7 · p. 24

VII. CONCLUSION

  • The proposed joint association and power-allocation scheme is guaranteed to converge; fixed-association power allocation uses feasibility conditions and a low-complexity optimal algorithm.The paper also derives analytical solutions for two-user clusters under both SIC orders.Source: §VII · p. 24
  • Each user can access only one RB in this work; extending the setting to multiple RBs is left for future work.Source: §VII · p. 24

APPENDIX A PROOF OF TABLE I

The proof checks theorem conditions across the power-allocation phases, then bounds user 2's power using QoS and maximum-power constraints.

APPENDIX A PROOF OF TABLE I

  • The proof verifies the conditions for Theorem 2 in Phases I–III before deriving user 2's power allocation.Source: Appendix A · p. 25
  • For Phase I, increasing user 2's power also increases interference to user 1, so user 2's usable maximum is limited by user 1's QoS.Source: Appendix A · p. 25
  • In Phases II and III, user 2's power has a minimum-rate lower bound and an unconstrained optimum below its maximum-power limit.The proof compares the unconstrained optimum with the rate and power constraints.Source: Appendix A · p. 25

APPENDIX B PROOF OF TABLE II

The proof treats Phase I separately because its SIC-order change puts user 2 at full power, while Phases II and III reduce the allocation to a constrained one-variable search.

APPENDIX B PROOF OF TABLE II

  • In Phase I, the SIC-order change requires user 2 to transmit at full power, while user 1 must preserve user 2's QoS.Source: Appendix B · p. 25
  • In Phases II and III, constraining user 1's power by user 2's QoS reduces the problem to a single-variable function whose candidate optimum is a derivative root.The resulting user 1 power is related to user 2's power by P1 = kP2 + b.Source: Appendix B · p. 25
  • The feasible user 2 power must satisfy user 1's own QoS lower bound; above the candidate optimum, EE decreases.The proof treats the candidate optimum within the user-1 QoS range as the solution.Source: Appendix B · p. 25

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